Bernard Daniel
09/29/2024 · Primary School
Write the system of equations corresponding to the augmented matrix. Then perform the row operations \( R_{2}=-4 r_{1}+r_{2} \) and \( R_{3}=6 r_{1}+r_{3} \) on the given augmented matrix.
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The system of equations corresponding to the augmented matrix is:
\[
\begin{align*}
1x_1 + 2x_2 + 3x_3 &= 4 \\
5x_1 + 6x_2 + 7x_3 &= 8 \\
9x_1 + 10x_2 + 11x_3 &= 12
\end{align*}
\]
After the row operations \( R_{2} = -4R_{1} + R_{2} \) and \( R_{3} = 6R_{1} + R_{3} \), the new augmented matrix is:
\[
\begin{bmatrix}
1 & 2 & 3 & | & 4 \\
1 & -2 & -5 & | & -8 \\
15 & 22 & 29 & | & 36
\end{bmatrix}
\]
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